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Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…
We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise…
Reinforcement learning constantly deals with hard integrals, for example when computing expectations in policy evaluation and policy iteration. These integrals are rarely analytically solvable and typically estimated with the Monte Carlo…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…
The Hamiltonian Monte Carlo (HMC) method allows sampling from continuous densities. Favorable scaling with dimension has led to wide adoption of HMC by the statistics community. Modern auto-differentiating software should allow more…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
Probabilistic programs with mixed support (both continuous and discrete latent random variables) commonly appear in many probabilistic programming systems (PPSs). However, the existence of the discrete random variables prohibits many basic…
We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…
This paper presents two novel ensemble domain decomposition methods for fast-solving the Stokes-Darcy coupled models with random hydraulic conductivity and body force. To address such random systems, we employ the Monte Carlo (MC) method to…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
A physical model based on a Monte-Carlo approach is proposed to calculate the ionization dynam- ics of warm dense matters (WDM) within particle-in-cell simulations, and where the impact (col- lision) ionization (CI), electron-ion…
Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions.…
When implementing model predictive control (MPC) for hybrid systems with a linear or a quadratic performance measure, a mixed-integer linear program (MILP) or a mixed-integer quadratic program (MIQP) needs to be solved, respectively, at…
Practical structural engineering problems are often characterized by significant uncertainties. Historically, one of the prevalent methods to account for this uncertainty has been the standard Monte Carlo (MC) method. Recently, improved…
Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…
How similar are two images? In computational pathology, where Whole Slide Images (WSIs) of digitally scanned tissue samples from patients can be multi-gigapixels in size, determination of degree of similarity between two WSIs is a…
Monte Carlo (MC) integration has been employed as the standard approximation method for the Sliced Wasserstein (SW) distance, whose analytical expression involves an intractable expectation. However, MC integration is not optimal in terms…
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for addressing the numerical sign problem. It resolves the ergodicity issues commonly encountered in Lefschetz thimble-based…
Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional…